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Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  23

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Answer: the correct answer is ='0'

Hint: y=\cos \left(\sin x^{2}\right) \frac{d}{d x} \sin x=-\cos x

       \frac{dy}{d x}=-\sin \left(\sin x^{2}\right)-\cos x^{2} \cdot 2 x

Given: y=\cos \left(\sin x^{2}\right)

Solution:  using \frac{dy}{dx} to get the value at \frac{\lambda }{2}

Now at x=\sqrt{\pi / 2}

\frac{d}{d x}=-\sin \left(\sin \sqrt{\frac{\pi}{2}}\right) \cdot \cos \sqrt{\frac{\pi}{2}} \cdot 2 \sqrt{\frac{\pi}{2}}=0

So the correct answer is ‘0'

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